source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Algorithms.Bandits/Policies/UCB1TunedPolicy.cs @ 11711

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace HeuristicLab.Algorithms.Bandits {
  public class UCB1TunedPolicy : BanditPolicy {
    private readonly int[] tries;
    private readonly double[] sumReward;
    private readonly double[] sumSqrReward;
    private int totalTries = 0;
    public UCB1TunedPolicy(int numActions)
      : base(numActions) {
      this.tries = new int[NumActions];
      this.sumReward = new double[NumActions];
      this.sumSqrReward = new double[NumActions];
    }

    private double V(int arm) {
      var s = tries[arm];
      return sumSqrReward[arm] / s - Math.Pow(sumReward[arm] / s, 2) + Math.Sqrt(2 * Math.Log(totalTries) / s);
    }


    public override int SelectAction() {
      int bestAction = -1;
      double bestQ = double.NegativeInfinity;
      for (int i = 0; i < NumActions; i++) {
        if (tries[i] == 0) return i;
        var q = sumReward[i] / tries[i] + Math.Sqrt((Math.Log(totalTries) / tries[i]) * Math.Min(1.0 / 4, V(i))); // 1/4 is upper bound of bernoulli distributed variable
        if (q > bestQ) {
          bestQ = q;
          bestAction = i;
        }
      }
      return bestAction;
    }
    public override void UpdateReward(int action, double reward) {
      totalTries++;
      tries[action]++;
      sumReward[action] += reward;
      sumSqrReward[action] += reward * reward;
    }
    public override void Reset() {
      totalTries = 0;
      Array.Clear(tries, 0, tries.Length);
      Array.Clear(sumReward, 0, sumReward.Length);
      Array.Clear(sumSqrReward, 0, sumSqrReward.Length);
    }
  }
}